On Hardy's theorem on SU(1,1)

The classical Hardy theorem asserts that f and its Fourier transform (f) over cap can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many "good" functions in the sense that f and its spherical Fourier transform (f) over tilde both have good decay. In this paper, we shall characterize such functions on SU(1, 1).MathematicsSCI(E)中国科技核心期刊(ISTIC)中国科学引文数据库(CSCD)0ARTICLE4429-4402